de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

implicit (dy)/(dx),e^{5y^2}=x^3+3

Lösung

implizite ableitung

\frac{d y}{d x}, e^{5 y^{2}} = x^{3} + 3

Lösung

\frac{d y}{d x} = \frac{3 x ^{2}}{e ^{5 y^{2}} \cdot 10 y}

Schritte zur Lösung

e^{5 y^{2}} = x^{3} + 3

Behandle

y

wie

y (x)

Beide Seiten differenzieren:

e^{5 y^{2}} \cdot 10 y \frac{d y}{d x} = 3 x^{2}

Isoliere

\frac{d y}{d x} : \frac{d y}{d x} = \frac{3 x ^{2}}{e ^{5 y^{2}} \cdot 10 y}

\frac{d y}{d x} = \frac{3 x ^{2}}{e ^{5 y^{2}} \cdot 10 y}

Beliebte Beispiele

y^'=(x-2)e^{-2y},y(2)=ln(2)

y^{^{'}} = (x - 2) e^{- 2 y}, y (2) = ln (2)

(\partial)/(\partial y)(xe^{x/y})

\frac{\partial}{\partial y} (x e^{\frac{x}{y}})

integral from 25 to 50 of 20

\int_{25}^{50} 20 d x

derivative f(x)=(x^2+1)/(x+4)

d er i v a t i v e f (x) = \frac{x ^{2} + 1}{x + 4}

derivative f(x)=x^{5/2}(2-5x^3)

d er i v a t i v e f (x) = x^{\frac{5}{2}} (2 - 5 x^{3})